Introduction to ARPES Seeing the superconducting gap Conclusion

ARPES: Uncovering the Superconducting GapPresentation for PHY601

Victor Drouin-Touchette1

1Department of Physics and AstronomyRutgers University

December 13th, 2017

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Introduction to ARPES Seeing the superconducting gap Conclusion

Outline

Introduction to ARPES

Seeing the superconducting gap

Conclusion

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Introduction to ARPES Seeing the superconducting gap Conclusion

Photoelectric effect

Shining light on a metal expulses photoelectrons;Can measure their kinetic energy. Does not depend on lightintensity IRather, depends on frequency ν

Ekin ∝ ~ν − const

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Introduction to ARPES Seeing the superconducting gap Conclusion

Einstein comes in: quantization of lightThe constant is actually the work function φ: energy todelocalize electron from surface.

Ekin = ~ν − φ

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Introduction to ARPES Seeing the superconducting gap Conclusion

ARPES: theory

Angular Resolved Photo-Emission SpectroscopyThe gist of it:

Want to measure energy of released electrons Ek andtheir momentum kUse conservation laws and photoelectric effect to extractinfo

Ekin = ~ν − φ− |EB| (1)p‖ = ~k‖ =

√2mEkin sin θ (2)

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Introduction to ARPES Seeing the superconducting gap Conclusion

Ekin = ~ν − φ− |EB|p‖ = ~k‖ =

√2mEkin sin θ

Ekin measured kinetic energy of outgoing electronθ measured is the angle of emission with the surfaceν and φ are knownEB wanted binding energy of electron in metalk‖ wanted crystal momentum

If one has that, we can construct the dispersion of the electronsE (k)!

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Introduction to ARPES Seeing the superconducting gap Conclusion

From Many-Body interpretation

Using ARPES, we measure the actual dispersion relation.Interactions (e-e, e-ph, etc) change band dispersions andlifetimes (spread)Measure the spectral intensity: I(k, ω)

Spectral intensity I(k, ω) ∝ f (ω)A(k, ω)

1p spectral func. A(k, ω) = − 1π

Σ′′(k, ω)[ω − εk − Σ′(k, ω)]2 + [Σ′′(k, ω)]2

bare band εk

Self-energy Σ(k, ω) = Σ′(k, ω) + i Σ′′(k, ω)= Band position + Linewidth/lifetime of QP

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Introduction to ARPES Seeing the superconducting gap Conclusion

Free electron v.s. Fermi Liquid

ARPES can see difference between a non-interactingelectron system and a Fermi Liquid system.In NI A(k, ω) = δ(ω − εk)Extremely sharp → Infinite lifetime of QPIn FL A(k, ω) = Zk

Γk/π(ω−εk )2+Γ2

k+ Aincoherent

QP peak has a width: finite lifetime τk = 1/Γk

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Introduction to ARPES Seeing the superconducting gap Conclusion

(Left) Theoretical band for Electron Phonon coupling, see thequasiparticle peak, which has a Lorentzian lifetime. (Right)Example of observed Arpes intensity for Bi2201

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Introduction to ARPES Seeing the superconducting gap Conclusion

Experimental Considerations

Need a very clean surface (atomically flat). Hencesurface-sensitive probe, not good on bulk! (probe∼ 2− 20Å in depth)Need ultra-high vacuum (avoid surface deterioration)Does not work under pressure or magnetic field.

However, very good at:Comparison to theoryHigh resolution in energy AND momentum

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Introduction to ARPES Seeing the superconducting gap Conclusion

Bad surface

Figure: Experiments on optimally doped Bi2212 (a) Dispersion right aftercleaving. (b) After 1h in pure nitrogen. (c) After 1h in air.

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Introduction to ARPES Seeing the superconducting gap Conclusion

A clean example: Cu

We see the εk = k2

2m∗ the free dispersion of Copper. The splittingof the bands can even be observed, due to Rashba coupling(spin-momentum locking, small but non-zero in Cu[111]).

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Introduction to ARPES Seeing the superconducting gap Conclusion

Outline

Introduction to ARPES

Seeing the superconducting gap

Conclusion

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Introduction to ARPES Seeing the superconducting gap Conclusion

Superconductivity Essentials

◦ Cooper instability: small attractive interaction binds electronstogether |k ↑,−k ↓>◦ In BCS theory, superconductivity is result of condensation ofthe Cooper pairs.◦ Conventional SC: attraction is due to retardedelectron-phonon interaction. Isotropic interaction.

H =∑

kξkc†k↑ck↑ + ξkc†k↓ck↓ + ∆c†k↑c

†−k↓ + ∆c−k↓ck↑ (3)

ξk = ~2k2

2m − µ (4)

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Introduction to ARPES Seeing the superconducting gap Conclusion

What is the gap

◦ Because of the pairing state, there is an energy gap for singleparticle excitation.◦ In a superconductor, there is a one-particle gap but notwo-particle gap.◦ The two-particle excitations (Cooper pairs) are coherent andtransport current without resistance.

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Introduction to ARPES Seeing the superconducting gap Conclusion

Example: Niobium

We can probe the DOSclose to the Fermi Surfacefor Niobium (Tc = 9.26K )For T > Tc , no peak belowEF , normal Fermidistribution.For T < Tc , gap opens,superconductivity sets in.

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Introduction to ARPES Seeing the superconducting gap Conclusion

S-Wave vs D-Wave

◦ In conventional SC,attractive interaction due toe-ph coupling: isotropic.Leads to s-wave pairing(gap positive all around FS).◦ In Cuprates, a d-wavepairing was advanced toexplain how they could haveSC behavior.◦ D-wave → has nodes where

∆(k) = 0 on the FermiSurface

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Introduction to ARPES Seeing the superconducting gap Conclusion

Bi-2212: Fermi Surface

◦ Bi2212: Bi2SR2CaCu2O8+δ,T max

c = 96K .◦ Planes of CuO with “stuff”in between. Fermi surface issimilar to YBCO (as inhomework)

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Introduction to ARPES Seeing the superconducting gap Conclusion

Bi-2212: Gap across FS

◦ Using ARPES, theexcitations near theFermi-Surface can be probedvery accurately.◦ Doing different cuts in

k-space, we can probedifferent parts of theFermi-Surface.

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A clear node

EF from polycrystalline metal. Gap is hard to read, but is there! 20 / 24

Introduction to ARPES Seeing the superconducting gap Conclusion

What to take from this

Exceptional resolution of the electronic structure (Bands &Fermi Surface);Can explicitly probe the gap;Answered many questions about the nature of the electronicexcitations in Cuprates (ex: gap symmetry + deviations);In Cuprates, has been very important to ascertain thepresence of the pseudogap phase (gap but no SC);To be used even more: Need materials with better surfacecleaving (currently being applied to pnictides Fe-based SC)

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Introduction to ARPES Seeing the superconducting gap Conclusion

Outline

Introduction to ARPES

Seeing the superconducting gap

Conclusion

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Introduction to ARPES Seeing the superconducting gap Conclusion

References

Liu et al. Rev. Sci. Instrum. 79(2), 023105 (2008)Tamai et al. PRB 87, 075113 (2013)Damascelli, Hussain, Shen. Rev. Mod. Phys. 75 473 (2003)Damascelli. Physica Scripta. Vol. T109, 61–74, 2004A. Chainani et al., PRL 85 (2000)I. M. Vishik et al. PNAS 109 (45) 18332–18337 (2012)

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Introduction to ARPES Seeing the superconducting gap Conclusion

Thanks for listening!

Questions?

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